Counting roots of the characteristic equation for linear delay-differential systems

被引：52

作者：

Hassard, BD

机构：

[1] Department of Mathematics, SUNY at Buffalo, 106 Diefendorf Hall, Buffalo

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 1997年 / 136卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1006/jdeq.1996.3127

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A formula is given that counts the number of roots in the positive half plane of the characteristic equation for general real constant coefficient, linear delay-differential systems. The formula is used to establish necessary and sufficient conditions for asymptotic stability of the zero solution of linear delay-differential systems. The formula is potentially useful in verifying stability hypotheses that arise in bifurcation analysis of autonomous delay-differential system. Application of the formula to Hopf bifurcation theory for delay-differential systems is discussed, and an example application to an equation with two delays is given. (C) 1997 Academic Press.

引用

页码：222 / 235

页数：14